It's the "automatic" part, combined with the implicit "every unit" at the start ("A race of monsters where every individual has an automatic counter..."), that makes this unworkable. It should have been, "Sure, killing one Cube is easy. But the second will probably have a perfect counter to the way you killed the first, so start getting creative quick!"

Then there's the fact that there's only so much room in a Cube: if the Borg know that a particular Cube is going up against a particular ship, the Cube (in theory) cannot be beaten by that ship because it will have perfect counters to everything they can anticipate that ship doing, but that leaves it vulnerable to third parties and unexpected desperation ploys.

Also also, there should be some things that even the Borg cannot tank: extreme tidal forces, being the "matter" part of a matter-antimatter reaction, the interior conditions of stars... (Antimatter is probably the easiest to weaponise. Develop a magbottle device designed to automatically shut down on being sent via transporter (or some environmental trigger) and put a kilo of antimatter in it. Then, whenever a Cube drops transporter barriers to send drones somewhere, beam over your little gift. This is assuming that antimatter is beamable, but why wouldn't it be?)

All that said, it's really a case of genre mismatch: as designed, the Borg were not designed for Star Trek (or at least, not designed to be a recurring antagonistic force in the TV shows). They belonged in their own work of fiction, one that revolves around humanity's attempts to understand, negotiate with, fight off, and ultimately flee this unstoppable alien force all proving futile. This is not helped at all by the fact that they underwent rapid decay, going from "alien beings with intelligence but without individuality or hierarchy, who will make you part of them because they genuinely believe that it's in your best interests and cannot be persuaded otherwise" (speaking of obstinacy, it would be very difficult to persuade me that this was not the original intent) to "brainless cybernetic zombie apocalypse that automatically wins until the writers do an asspull" within minutes of appearing on screen, if not before. They then descended quickly to "malevolent cyborg eusocial insects that automatically win until the writers do an asspull", which I find even less interesting than the cybernetic zombie apocalypse version.

EDIT:Oh, I got so caught up in that that I forgot to say how much I love this story. It's hilarious and perfect. These guys seem to be much better adjusted than the Datacommune mentioned in Cybertron Welcomes Careful Fliers.